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You searched for +publisher:"Boston College" +contributor:("Solomon Friedberg"). Showing records 1 – 2 of 2 total matches.

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Boston College

1. Cai, Yuanqing. Theta representations on covering groups.

Degree: PhD, Mathematics, 2017, Boston College

Kazhdan and Patterson constructed generalized theta representations on covers of general linear groups as multi-residues of the Borel Eisenstein series. For the double covers, these representations and their (degenerate-type) unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for GL(r). In this thesis, we study two other types of models that the theta representations may support. We first discuss semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondly, we determine the unipotent orbits attached to theta functions, in the sense of Ginzburg. We also determine the covers for which these models are unique. We also describe briefly some applications of these unique models in Rankin-Selberg integrals for covering groups. Advisors/Committee Members: Solomon Friedberg (Thesis advisor).

Subjects/Keywords: covering group; doubling construction; Fourier coefficient; semi-Whittaker coefficient; Theta representation; unipotent orbit

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APA (6th Edition):

Cai, Y. (2017). Theta representations on covering groups. (Doctoral Dissertation). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:107492

Chicago Manual of Style (16th Edition):

Cai, Yuanqing. “Theta representations on covering groups.” 2017. Doctoral Dissertation, Boston College. Accessed August 11, 2020. http://dlib.bc.edu/islandora/object/bc-ir:107492.

MLA Handbook (7th Edition):

Cai, Yuanqing. “Theta representations on covering groups.” 2017. Web. 11 Aug 2020.

Vancouver:

Cai Y. Theta representations on covering groups. [Internet] [Doctoral dissertation]. Boston College; 2017. [cited 2020 Aug 11]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107492.

Council of Science Editors:

Cai Y. Theta representations on covering groups. [Doctoral Dissertation]. Boston College; 2017. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107492


Boston College

2. Leslie, Spencer. Theta liftings on higher covers of symplectic groups.

Degree: PhD, Mathematics, 2018, Boston College

We study a new lifting of automorphic representations using the theta representation ϴ on the 4-fold cover of the symplectic group, \Sp̅2r(\A). This lifting produces the first examples of CAP representations on higher degree metaplectic covering groups. Central to our analysis is the identification of the maximal nilpotent orbit associated to ϴ. We conjecture a natural extension of Arthur's parameterization of the discrete spectrum to \Sp̅2r(\A). Assuming this, we compute the effect of our lift on Arthur parameters and show that the parameter of a representation in the image of the lift is non-tempered. We conclude by relating the lifting to the dimension equation of Ginzburg to predict the first non-trivial lift of a generic cuspidal representation of \Sp̅2r(\A). Advisors/Committee Members: Solomon Friedberg (Thesis advisor).

Subjects/Keywords: Arthur parameters; automorphic representations; CAP representations; metaplectic group; theta correspondence

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Leslie, S. (2018). Theta liftings on higher covers of symplectic groups. (Doctoral Dissertation). Boston College. Retrieved from http://dlib.bc.edu/islandora/object/bc-ir:107937

Chicago Manual of Style (16th Edition):

Leslie, Spencer. “Theta liftings on higher covers of symplectic groups.” 2018. Doctoral Dissertation, Boston College. Accessed August 11, 2020. http://dlib.bc.edu/islandora/object/bc-ir:107937.

MLA Handbook (7th Edition):

Leslie, Spencer. “Theta liftings on higher covers of symplectic groups.” 2018. Web. 11 Aug 2020.

Vancouver:

Leslie S. Theta liftings on higher covers of symplectic groups. [Internet] [Doctoral dissertation]. Boston College; 2018. [cited 2020 Aug 11]. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107937.

Council of Science Editors:

Leslie S. Theta liftings on higher covers of symplectic groups. [Doctoral Dissertation]. Boston College; 2018. Available from: http://dlib.bc.edu/islandora/object/bc-ir:107937

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